The standard BDDC (balancing domain decomposition by constraints) preconditioner is shown to be equivalent to a preconditioner built from a partially subassembled finite element model. This results in a system of linear algebraic equations which is much easier to solve in parallel than the fully assembled model; the cost is then often dominated by that of the problems on the subdomains. An impo...

A balancing domain decomposition (BDD) method is considered as a preconditioner of the iterative domain decomposition method (DDM) for magnetostatic problems. The BDD method enables us to keep convergence properties of the iterative DDM even if the number of subdomains increases. However, in case of magnetostatic problems, the dimension of the coarse problem required in the BDD procedure depend...

A three-level domain decomposition is considered. Bodies in contact with each other are divided into subdomains, which in turn are the union of elements. Using an approach based purely on FETI (finite element tearing and interconnecting) algorithms with only Lagrange multipliers as unknowns, which has been developed by the engineering community, does not lead to a scalable algorithm with respec...

in this paper we investigate decompositions of submodules in modules over a proufer domain into intersections of quasi-primary and classical quasi-primary submodules. in particular, existence and uniqueness of quasi-primary decompositions in modules over a proufer domain of finite character are proved. proufer domain; primary submodule; quasi-primary submodule; classical quasi-primary; decomposi...

This report describes a domain decomposition method for the incompressible NavierStokes equations in general coordinates. Domain decomposition techniques are needed if we want to solve ows in complex geometries. The discretization is performed by a nite volume method combined with a staggered grid arrangement. The domain decomposition technique is of Schwarz type combined with a GMRES accelerat...

In this paper, we shall solve a long-standing open problem: Is it possible that the convergence rate of the Lions’ Robin-Robin nonoverlapping domain decomposition(DD) method is independent of the mesh size h? We shall design a two-parameter Robin-Robin domain decomposition method. It is shown that the new DD method is optimal, which means the convergence rate is independent of the mesh size h. ...

in this paper, elzaki homotopy perturbation method is employed for solving linear and nonlinear differential equations with a variable coffecient. this method is a combination of elzaki transform and homotopy perturbation method. the aim of using elzaki transform is to overcome the deficiencies that mainly caused by unsatised conditions in some semi-analytical methods such as homotopy perturbat...

We develop a quasi-two-level, coarse-mesh-free characteristic nonoverlapping domain decomposition method for unsteady-state convection-diffusion partial differential equations in multidimensional spaces. The development of the domain decomposition method is carried out by utilizing an additive Schwarz domain decomposition preconditioner, by using an Eulerian-Lagrangian method for convection-dif...

In this paper the Smith factorization is used systematically to derive a new domain decomposition method for the Stokes problem. In two dimensions the key idea is the transformation of the Stokes problem into a scalar bi-harmonic problem. We show, how a proposed domain decomposition method for the bi-harmonic problem leads to a domain decomposition method for the Stokes equations which inherits...